Substitution in Lambda Calculus Lecture Notes

We study the formalization of lambda calculus based on De Bruijn terms. The most interesting aspect is a system of substitution primitives and an accompanying equational theory providing for algebraic proofs. The equational theory can be presented as a confluent and terminating rewriting system providing for proof automation. We prove that parallel reduction is strongly substitutive, the key property needed for the proof of the Church-Rosser theorem.